Forces and Free-Body Diagrams

The forces you cannot see

• A book lies still on a table — so nothing is happening, right?
• Wrong: gravity pulls it down and the table pushes it up, in perfect balance.
• Every object is a tug-of-war of hidden forces.
• To solve any mechanics problem, you first have to draw those forces.

What a force is

• A force 力 is a push or a pull one object exerts on another, measured in newtons.
• Contact forces 接触力 need touching — the normal force, friction, tension.
• Field forces 场力 act at a distance — gravity is the everyday one.

A free-body diagram 受力图 shows every force acting on one object

Draw a free-body diagram

• A free-body diagram shows the object as a single dot.
• Every force on it becomes an arrow, pointing the right way, labeled.
• Draw only the forces acting on the object — never the forces it exerts on other things.

Resolve into components

• Forces rarely line up with your axes, so split each into components 分量.
• On a ramp, tilt the axes along and across the slope.
• Gravity then splits into $mg\sin\theta$ down the slope and $mg\cos\theta$ into it.

Add them to a net force

• The net force 合力 is the vector sum of every arrow.
• Add components axis by axis: $\sum F_x$ and $\sum F_y$ separately.
• That net force is what $\sum F = ma$ then turns into acceleration.

Write from a net force of 7 N

• The horizontal forces are +8 N, -3 N and +2 N.
• Find the net force.